Modeling practice seems to be partitioned into scientific models defined by mechanistic differential equations and machine learning models defined by parameterizations of neural networks. While the ability for interpretable mechanistic models to extrapolate from little information is seemingly at odds with the big data “model-free” approach of neural networks, the next step in scientific progress is to utilize these methodologies together in order to emphasize their strengths while mitigating weaknesses. In this talk we will describe four separate ways that we are merging differential equations and deep learning through the power of the DifferentialEquations.jl and Flux.jl libraries. Data-driven hypothesis generation of model structure, automated real-time control of dynamical systems, accelerated of PDE solving, and memory-efficient deep learning workflows will all shown to be derived from this common computational structure of … READ MORE

I obsess over code performance, probably a little bit too much. But there’s a big reason for wanting a code to run in less than an hour instead of slightly more than two hours. The reason is because a code’s speed interacts with how we go about our day, and this speed can have a nonlinear effect on our productivity.

Here’s a concrete example. When I was a PhD student, I had a project which was solving ensembles of stochastic partial differential equations which were a model of the zebrafish hindbrain. Each run of this ensemble took about two hours and ten minutes to perform. For a good chunk of time, I needed to keep running these ensembles in order to manually check the output to tweak the model until it started to look realistic. Tweaking the model took only a … READ MORE

I did a livestream tutorial for solving differential equations in Julia and thought I should archive this in my blog. I hope this is interesting.

I think I am going to stop posting on Julia for a little bit. I looked at JuliaBloggers.com and realized my blog is hogging it to much. Since I have gone through a pretty good arc, starting at writing FEM code to multiple GPU / Xeon Phi computing, I think that means I will focus on a few other topics for a little bit. However, I will be doing a blog post on native Xeon Phi usage via Julia’s ParallelAccelerator.jl sometime soon, so be prepared for that.

In the meantime, stay tuned for topics like stochastic numerics, theoretical biology, Mathematica, and HPCs in the near future.

If you have the time, start up your own Julia blog and start contributing to JuliaBloggers!